Convertible vehicles are known in which the top has a sunroof part in its front region. The sunroof part is displaceable to the rear with respect to the surrounding top regions. To open the entire top, the sunroof part is initially opened while the rest of the top remains closed. After the sunroof reaches its completely open position, the top is then moved to an open convertible position. As such, opening the top from the closed position, when the sunroof is also closed, is very time consuming.